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I want to be sure that the way I like to think about the displacement method of analysis is correct.

Suppose that a beam as given by the figure in the link ( http://www.engineeringcorecourses.com/solidmechanics2/C7-deflection-of-beams-and-shafts/C7.1-superposition-method/example/ ) is to be solved.

Under this conditions, the only unknown is the rotation of joint B, that I'll denote X.
As I see it, the steps taken to compute X are:

i) apply a moment at point B of the beam such that no rotation of B takes place. Such a moment is clockwise. Due to this, node B is under the action of an equal and opposite moment of anticlockwise direction and, therefore, according to the standard conventions, of positive value PL/8, and, as such, not in equilibrium;

ii) for node B to be in equilibrium, as it effectively is in the original structure, apply at the right-end of the beam a moment whose value will depend of angle whose value we want to find ; Node B will be subject to an equal and opposite moment that is a function of X such that M(X)+ PL/8=0.

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